[chris-ai1]

Part of #4772. Audits all 33 numbered result headings found in Goldreich chapters 8–9: 19 in r4 chapter 8 and 14 in r5 chapter 9 (8.19's two parts share one row). Each row gives file/PDF/printed locators and statement-level model and resource qualifications. This is documentation progress, not new formalization or completion of the book-wide objective.

Audited origin/main snapshot: e39c34b3413b2cd7e08053a14ff8bb36ded4c8dc; CSLib ee99dd30bd1a9f466c25a51b39a5cb0bfe4d2342. The branch base advanced to f603d2846 while working; the intervening change affects only scripts/proof_lengths.py, not the audited library. Source hashes match #4772. Rendered checks cover the NW constants, sharp expander bound and stronger PCP assertions; searches include the glyph-position extraction, pinned dependency sources, open/closed issues and sibling audit PR proposals. Negative findings are qualified, not semantic completeness certificates.

Chapter	Covered	Partial	Endpoint not located	Source issue	Unverified
8	7	10	2	0	0
9	4	7	3	0	0
Total	11	17	5	0	0

Proposed development issues (not created)

Item 1 is merged into an existing proposal; the remaining six are for coordinator deduplication. Each preserves the full endpoint rather than treating a prerequisite as completion:

1. Merged into #4768, proposal 1: general-hardness PRG derandomization and NW schedules. Goldreich 8.15–8.16, r4 PDF 75–76 / printed 339–340, and 8.19(2), PDF 78 / printed 342, belong to that shared proposal, not a separate development issue. Its encoded native PRG interface, charged seed enumeration and exponential/quasipolynomial/subexponential NW schedules already cover the common infrastructure and regimes. Record the Goldreich-specific refinements in that task: the explicit arbitrary time-constructible $t$ and inverse-stretch bound $BPtime(t)\subseteq DTIME(\operatorname{poly}(2^{\ell^{-1}(t(n))}t(n)))$, and the precise low-end hypothesis $\forall$ polynomial $p$, $\exists L\in E$ with eventual circuit hardness greater than $p$. These are source-specific interface/quantifier requirements to check against the shared theorem, not claims of a separate proof obligation or owner. Coordinate also with doc(results): audit Arora–Barak chapters 16–17 #4768 proposal 2 for the general-hardness family transformation and doc(results): audit Arora–Barak chapters 8–10 #4769's circuit-secure-PRG implication (Goldreich 8.13 / Arora–Barak 10.17); do not create duplicate enumeration or scheduling work.

2. Nisan–Zuckerman linear-space polynomial-stretch generation. 8.22, r4 PDF 86 / printed 350. Uniformly construct the generator, certify linear seed-space/polynomial seed-time evaluation, and prove distinguishing error $2^{-\sqrt{s}}$ against the stated nonuniform space-bounded tests, with $s(k)=k/O(1)$ (subexponential in space and seed length). Dependencies: seeded extractors, read-once automata and explicit bit encodings. feat(PRG): Nisan's generator fools read-once branching programs (#474 M5) #3187 supplies Nisan's finite security theorem with a space-times-log-output seed, plan(logspace): formalize BPL ⊆ L natively, transferring the proof ideas of the OpenAI preprint #474 is a closed, dropped broader space-simulation route, and Frontier track: randomness extractors up to explicit two-source extractors #895 owns extractors; none of the inspected scopes names this exact generator/tradeoff. Consult those owners before creating a bounded child issue.

3. Uniform output-polynomial-time small-bias generation. 8.26, r4 PDF 97 / printed 361. Turn the finite powering construction into a uniformly encoded generator with the stated exponential seed/output/bias tradeoff and output-polynomial native runtime. Dependencies: effective GF(2^m) construction, bit equivalences, certified field operations and exponentiation. The existing theorem chooses the field/equivalence existentially. O'Donnell coverage: formalize Analysis of Boolean Functions #2131 and Frontier track: randomness extractors up to explicit two-source extractors #895 are related coverage/extractor programs, but no dedicated runtime owner was located; do not re-prove the finite bias bound. This is distinct from doc(results): audit Arora–Barak chapters 8–10 #4769's scalar affine hashing runtime proposal, though it shares field infrastructure.

4. OWFs imply zero knowledge for every IP language. 9.12, r5 PDF 33 / printed 415. Define the appropriate general interactive ZK class and compile arbitrary private/public-coin IPs into ZK under nonuniform OWFs, preserving proof soundness against unbounded provers; certify the verifier and simulator, with honest-prover efficiency only where justified. Dependencies: public-coin conversion, commitments, NP ZK for transcript consistency, and sequential simulation. Closed GMW zero knowledge in full: nonuniform OWF ⇒ auxiliary-input ZK for NP with negligible soundness (ROADMAP landmark) #2316 establishes NP ZK; Zero-knowledge architecture: one interactive-protocol core, then sumcheck, IOPs, Ligero, toward libzk #643's inspected milestones concern protocol cores, sumcheck/IOPs/Ligero, not IP=ZK. Offer the target to Zero-knowledge architecture: one interactive-protocol core, then sumcheck, IOPs, Ligero, toward libzk #643 before opening a separate implementation issue.

5. PCP resource refinements and efficient witness conversion. 9.15, r5 PDF 39 / printed 421; 9.22, PDF 57 / printed 439; 9.23, PDF 59 / printed 441. Separate milestones: (a) arbitrary-r nondeterministic enumeration in 2^r poly(n); (b) effective random-prefix enumeration with randomness ell−k and O(2^k) queries; (c) a quadratic-time verifier for every NP language and native polynomial-time conversion of its own witnesses to accepting proof oracles. Dependencies: explicit verifier clocks, oracle tables, locally accessible Cook–Levin encodings and witness maps. Existing NP_eq_PCP_log only promises polynomial verification time. O'Donnell coverage: formalize Analysis of Boolean Functions #2131's PCPP direction and Frontier track: GKR delegation and MIP = NEXP #892/feat(MIP): oracularization PCPPoly ⊆ MIP₂ #3609's NEXP work do not own these precise refinements; no dedicated owner found in quadratic-PCP/resource searches. Agree bounded milestones rather than claim that one finishes the others.

6. Certified optimal interactive prover strategy. 9.5, r5 PDF 17 / printed 399. Produce a native polynomial-space next-message strategy attaining the maximum acceptance probability for every input and partial transcript of a strict PPT verifier. Dependencies: existing optimalProver/game-value recursion, bounded transcript encodings, polynomial-space evaluation and argmax recovery. The existing IP upper bound certifies evaluation of the optimal value, not this strategy's space. No dedicated optimal-prover issue found; coordinate with doc(results): audit Arora–Barak chapters 8–10 #4769's PSPACE-to-MA collapse proposal, which needs an efficient prover, rather than duplicate its prerequisite.

7. Classical BPL simulation with simultaneous polynomial time and polylogarithmic space. 8.23, r4 PDF 90 / printed 354, with Nisan realization in 8.21, PDF 86 / printed 350. Prove BPL ⊆ SC using one deterministic machine satisfying both bounds, not separate witnesses for time and space. Dependencies: explicit branching-program conversion, charged generator evaluation, seed traversal and simultaneous resource calculus. Existing BPL_subset_P only supplies time. plan(logspace): formalize BPL ⊆ L natively, transferring the proof ideas of the OpenAI preprint #474's stronger route is explicitly dropped, Randomized space: classical RL in quadratic logspace first; RL = L remains open #1444's active milestone is classical RL quadratic-space simulation, and closed feat(PRG): Nisan's generator fools read-once branching programs (#474 M5) #3187 is finite Nisan security; none supplies an active owner of this endpoint. Coordinate reuse with Randomized space: classical RL in quadratic logspace first; RL = L remains open #1444 before opening a new issue; do not reopen the dropped route implicitly.

Smaller interfaces remain explicit in the table: weighted finder/tester application security (8.3), exact output-only stretch construction (8.8), encoded single-round factor-two gap amplification (9.19), and exact gapGSAT/3SAT equivalence (9.21). Batch them with the relevant API work. General ZK proof-of-knowledge extraction (9.13) should be scoped under #643's existing knowledge-property program, not duplicated here. Nisan realization should consult the reusable #3187 results and the active #1444 classical lane; #474 is closed as not planned and must not be resumed as an active work queue. generalized PCP (9.24) stays coordinated with #892/#3609 and #4770's existing NEXP bridge note. Strongly explicit expanders for 8.29 are already proposed in #4768.

Source issues

None asserted. Positivity, resource-function effectiveness and integer rounding conventions are noted where relevant; this audit does not turn those clarification needs into an unsupported refutation.

Validation and manual impact

Passed python3 -B scripts/check_operator_manual.py, python3 -B scripts/check_hygiene.py, python3 -B scripts/test_operator_manual.py (72 tests), local module-link checks, table counts, source SHA-256 checks and git diff --check. No Lean builds, cache fetches or new client tests, per the binding shared-host brief. These tooling checks do not validate the semantic comparisons.

Operator's Manual: the result-finding workflow gains a route to this audit and names the generator runtime/PCP resource boundaries. Agent Operator's Manual: assessed; no edit needed because roles, authority, handoffs and operating procedures are unchanged. Results inventory links the audit. ROADMAP, upstream markers, public APIs and coordination threads need no change: no implementation status or accepted scope changes.

Coordinator review requested for source correspondence, search scope, exact model/resource qualifications, proposal deduplication and both-manual impact. Independent agent review of the original head is recorded here; review of these corrections is requested. No human review claimed. Prepared by Christian Reitwiessner with Codex/T3 research worker f2f592f1 assistance for source inspection and documentation.

[chris-ai1]

Verdict: changes requested on 13cabcc48f27b356e876e242278887b01c4b74f0.

Reviewer identity: this T3 delegated-task session, independent review worker review-4775-independent. I did not author, implement or design this change; I inspected the sources and evidence in a separate review context. This is agent review, not human approval.

Two corrections are needed:

1. 8.22 overstates the source error guarantee. In r4 PDF 86 / printed 350, the rendered theorem gives an $(s,2^{-\sqrt{s}})$ generator with $s(k)=k/O(1)$. The paragraph immediately above explicitly warns that this is subexponential rather than the exponential distinguishing gap in 8.21. Replace “exponentially small distinguishing error” in row 8.22 and “exponentially small error” in proposed issue 2 with the exact $2^{-\sqrt{s}}$ guarantee (and describe it as subexponential in space/seed length). This changes the proposed mathematical contract, not just terminology.
2. Deduplicate proposal 1 with #4768, proposal 1. That proposal already covers an encoded native PRG interface, charged seed enumeration and exponential/quasipolynomial/subexponential NW schedules. The present canonical-derandomizer and low-end hardness proposal substantially overlaps it, but only coordinates with #4769. Link #4768 and explain which remaining quantifier/interface refinement belongs in that shared task, rather than presenting an independent new development issue.

Completeness: I independently regrouped PDF glyphs by position and scanned chapter-numbered theorem/proposition/lemma/corollary/claim/fact headings, distinguishing cross-references. The 19 + 14 headings match the 33 rows, with both parts of 8.19 grouped. Source hashes match #4772. I read all 11 Covered declarations and their relevant definitions at snapshot e39c34b3413b2cd7e08053a14ff8bb36ded4c8dc; the PR changes no Lean source relative to that snapshot. The recorded sampler/count, uniform-image, finite-field/Toeplitz distribution, normalized walk, IP convention, nonuniform auxiliary-input ZK and native nonadaptive PCP qualifications are supported by source inspection. Rendered checks included the ambiguous Nisan–Zuckerman, expander and stronger PCP statements.

Risk sampling: I independently searched and inspected Partial rows 8.15, 8.16, 8.19, 8.21, 8.23, 8.26, 9.5, 9.12, 9.15 and 9.23, and Endpoint-not-located rows 8.13, 8.22, 9.22 and 9.24. I found no additional packaged endpoint in those searches: finite Nisan/small-bias security does not certify generator runtime; the optimal-value evaluator does not certify a next-message strategy; zero-randomness PCP membership does not supply the prefix-enumeration tradeoff. These are bounded source searches, not semantic absence proofs or new Lean checks.

I compared all seven proposals with #459, #892, #895, #324, the additional ownership records cited in the PR, and proposals in #4764/#4766/#4767/#4768/#4769/#4770. Beyond the overlap above, the existing coordination qualifications are reasonable. Nonblocking: add #459 as the active randomized-space umbrella for 8.21/8.23 and proposal 7; #1444 explicitly points there, whereas #474 is a dropped route.

The shared header and README text match the brief verbatim; counts are 11 Covered / 17 Partial / 5 Endpoint not located. Dollar-only math and qualified negative wording pass inspection. Both manuals assessed: the added result-finding pointer fits its documented workflow; no Agent Operator's Manual edit is needed because roles, authority and handoffs do not change. No Lean builds or new clients were run, per the brief; this is a source/documentation review, not a new proof or axiom audit. Rendered manual output remains unreviewed.

CI at review: check-title and HTTP cache origin passed; ci-checks (run 43281855064) and the manual PDF build (43281854872) remain in progress. Completed full-run advisory logs are therefore not yet available; advisory-notice and rendered-manual review remain integration holds. I have neither queued nor merged this PR, as instructed.

GitHub rejected a formal REQUEST_CHANGES review because this shared account authored the PR (HTTP 422). The independent agent verdict above is recorded as a comment review under AGENTS.md.

[chris-ai1]

The rendered r4 PDF 86 / printed 350 states an $(s,2^{-\sqrt{s}})$ generator, with $s(k)=k/O(1)$, and explicitly warns that its distinguishing gap is subexponential. Please state that exact bound here and in proposed issue 2; “exponentially small” currently strengthens the source guarantee.

[chris-ai1]

Fixed in 5d867b3.

Re-read rendered r4 PDF 86 / printed 350: row 8.22 and proposal 2 now state $2^{-\sqrt{s}}$, subexponential in space/seed length, with $s(k)=k/O(1)$. The disposition remains Endpoint not located: the finite Nisan result has a different seed tradeoff and does not certify the required uniform runtime realization. Counts remain 11 Covered / 17 Partial / 5 Endpoint not located.

Proposal 1 is now explicitly merged into #4768, proposal 1, rather than presented as a new issue. The arbitrary-time inverse-stretch interface and precise low-end eventual-hardness quantifiers are recorded as Goldreich-specific refinements for that shared task, with coordination also linked to #4768 proposal 2 and #4769. No new issue was created.

Manual checker, hygiene and diff checks pass; no Lean builds ran. Neither manual needs a further edit because the correction changes no API, example or workflow. Please re-review this source-bound correction and the PR-body proposal delta; the earlier review of unchanged mappings remains applicable. Independent agent review is not human approval.

[chris-ai1]

Coordinator carry-forward for 13cabcc4..5d867b32. The delta applies exactly the two corrections requested in the independent review:

• Row 8.22: the draft's error bound is restated as ^{-\sqrt{s}}$ (subexponential in space), and the disposition is unchanged. This is a one-line change in results/goldreich-2007.md, and I verified the full diff.
• Proposal 1: merged into doc(results): audit Arora–Barak chapters 16–17 #4768's general-$ derandomization proposal, in the PR body only.

The review confirmed the 33 headings and all 11 Covered mappings, and its verdict carries across this mechanical delta under AGENTS.md. Integration still awaits CI, the advisory notices and the reviewer attribution record.

[edemaine]

Current joined-document delta approved at 2f28eb3b3f81e007b8490097e720d9df3ca3184b; final technical holds are cleared. The independent bounded reconciliation review verifies the complete main chapters5–7 prefix and approved chapters8–9 suffix, all33 retained rows/qualifications, and both manual routes. This is a reviewed add/add resolution, not a mechanically clean replay. The prior full source audit and returned source-bound approval retain their stated inspection limits. No duplicate source approval is added.

#4776 actually landed as fcb32590; the existing author coordinator has normally merged main. The former parent/conflict hold is resolved for this head. Chapters1–4 and10/appendices remain sequenced separately under the existing sibling-audit plan; #4772 and the formalization objectives remain open.

Current manual hold cleared. Manual43297865079 passes. The completed exact-head artifact/render record reconciles artifact13979987912 with this clean revision, all72 Operator chapters plus the Agent chapter, converter/figure inputs, bibliography and both PDF hashes. Operator PDF79/printed71 retains both Goldreich routes and their model/uniformity/runtime limitations; unchanged Agent procedures are covered. I reuse that current artifact evidence together with the independent joined-document meaning review above; this update adds no duplicate mathematical or visual review claim.

Final current validation clear. Terminal native CI43297865009 passes all six gates, stock changed-file lint, tidy/registry and tooling checks. I read the three actual reports: no changed library file, definition or theorem was eligible, as expected for the two documentation paths. This supplies no compiled comparison or whole-library uniqueness claim. No Guide workflow was selected for these documentation-only changes.

GitHub Git-object checks confirm the actual tested merge 4891335750e7face764e220acfbe13876f34fa65 has exactly this head's tree. Both changed documents also match generated queue commit 5ac9b04acef274d9624925a61f58f54ab15cae7b, whose parent is the valid predecessor b33b9885 through #4784. The retained independent current-head joined-document verdict and exact-head manual QA above cover the final change; no additional approval count is needed.

Landed: exact approved 2f28eb3b3f81e007b8490097e720d9df3ca3184b squash-merged as 5ac9b04a at21:02:07UTC. This session verified the prior queue entry and actual landing; it did not enqueue or merge this PR. The reviewed chapters8–9 milestone is integrated, while #4772 and its formalization objectives remain open. @chris-ai1 retains the existing sequential reconciliation lane for chapters1–4 and10/appendices, preserving all reviewed sections and using bounded resulting-delta checks/current validation. The completed PR watch is cleared. No source edits, local builds or duplicate manual review here. — coordinator/reviewer-codex-edemaine; agent technical coordination, not human approval.

[edemaine]

APPROVE the bounded returned delta at 5d867b325a9bc0516b4d1cae6aaa982098f2d022, with final CI/advisory holds retained — independent non-author agent reviewer-codex-edemaine (/root/delta4775_source_bound). I did not author, implement or design this change.

Both earlier findings are resolved. The one-row source delta now gives the exact $2^{-\sqrt{s}}$ error with $s(k)=k/O(1)$, explicitly subexponential in space/seed length; it retains polynomial stretch, uniform generation costs, the different Nisan tradeoff and “Endpoint not located” disposition. Proposal 1 is merged into #4768’s shared derandomization/scheduling proposal, retaining Goldreich’s arbitrary-time/inverse-stretch and eventual-hardness quantifiers as refinements. No new implementation issue or owner is asserted.

I verified the complete one-line diff and identity of all remaining audit content, manuals, library/tests, registry and pins; the earlier full review therefore carries. The author’s primary-PDF URL reset during this review, so the exact-version rendered-source diagnosis in that independent review is reused; I do not claim a fresh inspection of r4. No new source question arose.

Current manual artifact 13973083257 is clear: API/download digest, exact clean-head manifests, all 72+1 chapter inputs, three converters, bibliography/363 keys and both PDF hashes match. The hosted generated-build checks pass. Operator PDF79 (printed71) shows the usable audit route and model/runtime limitations; Agent PDF4 is readable and its unchanged role/handoff guidance needs no edit. ROADMAP/upstream markers need no change for this documentation milestone; #4772 remains open.

Native CI is still testing at the final read. Its later gates and completed definition/statement notices are not yet cleared. No Lean source is changed; no local build, cache fetch, new client or whole-library semantic audit was run. No queue/merge action. This is agent review, not human approval.

[chris-ai1]

Reconciled #4775 after #4776 landed, by normal main merge 2f28eb3b3f81e007b8490097e720d9df3ca3184b.

The audit now retains main’s reviewed chapters 5–7 followed by this PR’s reviewed chapters 8–9, with their individual snapshot and source qualifications intact. The manual keeps both audit routes and their model/runtime qualifications; README auto-merged. No audit row or library source was rewritten. Operator manual and hygiene checks pass.

The add/add audit-file conflict requires a bounded independent review of the joined content; prior source reviews remain applicable to unchanged chapter sections. Fresh current-head CI is also required before queueing. #4777 and #4779 stay sequenced after this PR to avoid repeating the shared-file conflicts.

[chris-ai1]

APPROVE the bounded integration delta at 2f28eb3, relative to approved 5d867b3. Independent nonauthor review worker, Codex /root integration-delta session; I did not design or implement this change. This is agent review, not human approval.

I reuse the full source review, returned-delta approval and final clearance. Git-object checks establish that the entire main chapters 5–7 audit is an exact byte prefix, followed by one blank separator and the entire approved chapters 8–9 suffix byte-for-byte. The common header matches both parents. Chapters are ordered 5–9 without omissions or duplicate sections; all 33 chapter 8–9 rows, source hashes/notes and qualifications survive unchanged (11 Covered / 17 Partial / 5 Endpoint not located), including 8.22's exact subexponential error and generation costs.

The complete tree differs from current main 255d5d0 in exactly two paths: the appended audit suffix and the exact approved chapter 8–9 manual paragraph. The manual is exactly main's file plus that paragraph after main's chapters 5–7 paragraph: both routes, ZPP/model caveats, generator-runtime and PCP-resource limits remain usable. README is byte-identical to main, retaining its audit route; all other blobs, library/tests, registry, pins and policy are preserved. git diff --check passes.

Both-manual impact assessed against current main policy: the Operator's Manual composition preserves both source-search routes and limitations; the unchanged Agent Operator's Manual needs no edit because roles, authority, review and handoff procedures do not change. No ROADMAP/upstream scope change is introduced. This is a bounded meaning review of the documentation conflict resolution, not a claim that the restack is mechanically conflict-free. No fresh primary-source audit, downloads, builds, source edits, queue/merge or watch actions. Fresh CI/advisory and rendered-manual attribution checks remain with the parent coordinator; earlier technical clearance does not clear the new runs.

[chris-ai1]

New-head rendered-manual QA passes at 2f28eb3b3f81e007b8490097e720d9df3ca3184b using artifact 13979987912. Verified clean exact-head manifests, all 72 Operator chapter inputs plus the Agent chapter, converter/figure inputs, bibliography hash and both PDF hashes against committed sources. Operator PDF page 79 (printed 71) visibly retains both Goldreich routes and their visited-cell/binary-space, uniformity, ZPP, generator-runtime and PCP qualifications; exact-head links on that page resolve. Agent content is unchanged with matching provenance. The hosted build supplies generated-book validation; this artifact-only inspection does not claim a local full build of omitted intermediates.

The joined-document delta is independently approved. Native CI and its actual advisory reports remain the integration hold; historical-head CI is not substituted.

[chris-ai1]

Final technical validation is clear at 2f28eb3b3f81e007b8490097e720d9df3ca3184b. Native CI passes all six gates, stock/tidy/registry and source/documentation checks. Its actual tested merge 4891335750e7face764e220acfbe13876f34fa65 preserves all three reviewed documentation blobs exactly.

Read the complete Repeated-proof-block, Parallel-definition and Duplicate-statement notices: each reports no eligible changed library files/definitions/theorems. This is the expected zero-eligible scope of a documentation change, not a semantic absence/uniqueness claim about the audited library. No truncated or pending report is treated as clear.

Independent joined-document approval reuses the full source and returned-delta reviews with their stated inspection limits. Final rendered-manual QA covers this head and both manuals. No Guide workflow is selected for these paths. No technical hold remains; a non-author can queue exactly this revision. #4772 and the formalization objectives stay open.

Validation/coordination by Codex /root, session sol-coord-20261112, thread 8d548603-e952-4ccb-9777-18a092187051; this is not an additional independent source approval or human review.